Answer
$$(x-6)(x+3)^2=x^3-27x-54$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-6)(x+3)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x-6)(x^2+6x+9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^3+6x^2+9x-6x^2-36x-54 \xlongequal{ } \\[1 em] & \xlongequal{ }x^3+ \cancel{6x^2}+9x -\cancel{6x^2}-36x-54 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-27x-54\end{aligned} $$ | |
| ① | Find $ \left(x+3\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ x } $ and $ B = \color{red}{ 3 }$. $$ \begin{aligned}\left(x+3\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 3 + \color{red}{3^2} = x^2+6x+9\end{aligned} $$ |
| ② | Multiply each term of $ \left( \color{blue}{x-6}\right) $ by each term in $ \left( x^2+6x+9\right) $. $$ \left( \color{blue}{x-6}\right) \cdot \left( x^2+6x+9\right) = x^3+ \cancel{6x^2}+9x -\cancel{6x^2}-36x-54 $$ |
| ③ | Combine like terms: $$ x^3+ \, \color{blue}{ \cancel{6x^2}} \,+ \color{green}{9x} \, \color{blue}{ -\cancel{6x^2}} \, \color{green}{-36x} -54 = x^3 \color{green}{-27x} -54 $$ |
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